Quote from: Vessko on January 31, 2015, 11:59:10 AM

The examples given here are wrong and misleading.

The problem is not that it is not possible to compute the private key, because there is more than one solution (like in the case of abs() or the sum of numbers). The problem is that it is possible, in theory, to compute it, but the computation is so hard that it is practically infeasible.

Do not confuse asymmetrical cryptography with hashes. A hash is impossible to reverse, because many different inputs can result in the same output. (It's just that there is no easy way of finding all of them - or even any one of them.) A private key can be computed from the public one - but it is very, very hard - hard enough to be practically impossible.

For instance, if I ask you what is the product of 31 and 37, the answer is easy - 1147. But if I ask you what are the prime factors of 1147, that's a hard question. The easiest way to answer it is by trial and error - you try to divide 1147 by every prime number smaller than the integer part of its square root until you find a number that divides it exactly (the first such number is 31). When the numbers involved are very large it becomes practically impossible to answer such questions. (With large numbers there are faster methods than trial division, but they are still too slow to be practical.)

The first few explanations gave me a conceptual idea, this explained everything.